Data Types: Numerical and Categorical Data

Data Types

• Data constitutes numbers, characters, text, images, audio, and video, and serves as the base for analysis, interpretation, and decision-making.
• Choosing proper analysis methods and visualizations requires distinguishing between data types:
  • Discrete data uses scatter plots.
  • Continuous data uses lines or curves.

Numerical Data

• Represents measured or counted quantities as a number.
  • Continuous data can take on any numerical value within a specified range (e.g., stock prices).
  • Discrete data is limited to a finite number of values (e.g., shares of a stock).

Categorical Data

• Describes qualities or characteristics which cannot be measured numerically, it involves classification and organization into groups, e.g., segmenting stocks into sectors
  • Nominal data: categories without inherent order (e.g., types of investment vehicles).
  • Ordinal data: categories with a logical order, but intervals are inconsistent or meaningless (e.g., credit ratings).

Applying Data Types

• Number of coupon payments for a corporate bond is discrete data.
• Cash dividends per share paid by a public company are continuous.
• Credit ratings for corporate bond issues are ordinal data.
• Hedge fund classification types are nominal data.

Data Organization Types

• Numerical vs. categorical data
• Cross-sectional vs. time-series vs. panel data
• Structured vs. unstructured data

Numerical VS Categorical

• Numerical data have values that represent measured or counted quantities called quantitative data and can be split ​​into 2 categories
  • Continuous data, is data that can be measured and take on any numerical value within a specified range of values.
  • Discrete data, is numerical values are a result from a counting process

Cross-Sectional Data

• Observations of a specific variable are taken from multiple observational units at a specific point in time.
• Observational units include individuals, groups, companies, trading markets, and regions.

Time-Series Data

• A sequence of observations of a specific variable is taken from a single observational unit over time.
• Taken at discrete intervals such as daily, weekly, monthly, annually, or quarterly.

Panel Data

• Is used for Financial analysis and modeling that incorporates time-series and cross-sectional data.
• Panel data includes for multiple observational units through time using one or more variables.

Cross-Sectional Versus Time-Series Versus Panel Data

• Cross-sectional data is collected at a single point in time and focuses on different entities. -Example is analysing the financial performance of different companies using their annual reports for a selected year.
• Panel data combines cross-sectional and time-series data.
  • Example is quarterly earnings per share for three companies in a given year by quarter.
• Time series data is collected over multiple time periods for a single entity
  • Example is tracking the monthly stock prices for a specific company.

Structured Data

• Organized such as one-dimensional arrays which is a time series of a single variable.
• Two-dimensional data tables where each column is a variable and each row is a set of values.
• Market data issued by stock exchanges is structured data.
• Fundamental data contained in financial statements is structured data.
• Analytical data is derived from analytics.

One-Dimensional Arrays

• Represents a single variable.
• Includes Daily Closing Price of ABC Inc. Stock

Two-Dimensional Arrays

• A popular form for organizing data, which is comprised of columns and rows.
• It comprises multiple variables and observations.
• Includes data tables for ABC Inc.

Frequency Distributions

• Summarizes data into groups or bins for interpretation, and evaluate the data distribution.
• Tabular data display, counting observations or tallying numerical variables into bins.
• A frequency distribution table facilitates finding patterns in a snapshot of the data.

Contingency Tables

• Display frequency distributions of two or more categorical variables.
• Used for finding patterns between variables.
• Illustrates portfolio frequencies by sector and market capitalization.

Data Visualization

• Presents data in a pictorial or graphical format in order to increase understanding and insights.
• Data visualization includes histograms, bar charts, tree maps, word clouds, line charts, scatter plots, and heat maps.

Histograms

• Charts showing distribution of numerical data.
• The height of a column represents absolute frequency of each bin or interval.
• Frequency polygons: graph of frequency distribution, straight lines connecting successive class frequencies.

Bar Charts

• Tool which expresses the frequency distribution of categorical data.
• Each bar is a distinct category: height is proportional to category frequency.

Tree-Map

• Colored rectangles represent distinct groups.
• Rectangle area represents value of the corresponding group.
• Used for hierarchical data and comparing proportions.
• Illustrates frequency distribution by sector in a portfolio.

Word Cloud

• Visual representation of textual data.
• Word size is proportional to text frequency.
• Allows for quick perception of frequent terms and topics.

Line Chart

• To visualize ordered observations.
• Shows trends and relationships over time.
• Daily closing prices of stocks and sector indices.

Scatter Plot

• Visuals joint variation in two numerical variables.
• Useful for displaying and understanding potential relationships between the given variables.
• To investigate relationships and correlations between two variables.
• Information technology sector Index return vs the index return from the Index Standard & Poor (S&P) 500.

Heat Map

• Graphic that organizes and summarizes data in a tabular format represented by a color spectrum.
• Contingency table that summarize the joint frequencies of stock holdings by sector.
• By level of market capitalization.
• Shows magnitude in two categorical variables.
• Includes frequencies by sector and market capitalization.

Selecting Visualizations

• The key consideration is the intended purpose.
• To explore/present distributions or relationships.
• To make comparisons.
• Best visualization is the simplest visual that conveys the message.
• Avoid: improper charts, plotting selectively, truncated graphs, and improper scaling.

Visualizations For the Following Goals

• To analyze daily trading volumes: use a histogram.
• To assess associations between numerous variables: use a scatter plot matrix.
• To understand the topic and sentiment of meeting minutes: use a word cloud.
• To compare quarterly revenues and earnings of two companies: use a bubble line chart.

Measures of Central Tendency

• These specify where the data are centered and it helps you understand where you financial data, like stock prices over a month all bulk Arithmetic mean, Geometric mean ,Weighted mean, Harmonic mean, Median, Mode, quartiles, quintiles, deciles, and , percentile

Measures of Central Tendency Continued

• Although frequency distributions, histograms, and contingency tables which provide an easy way to summarize several observations, is just the first step towards describe the data
• Central Tendency: specifying where the data is centered, there is probably a much amount of widely used then any other statistical measure.
• Measures of Location include measure of central tendency including other measures that illustrate the distribution of data
• Statistic, a summary of a sample observations
• Population are all the members of a specified group.
• Sample Statistic, statistics which summarizes a set of observations
• One number which describes a possible outcome of an investment decision the arthimetic mean is one of the most frequently used measure for the center data division
• Defined Arthemetic mean is the sum of the value divided by the number of observations made

Arithmetic Mean

• Determined by the sum of the values of the observations divided by the number of observations.
• Can be skewed and influenced by outliers.

Geometric Mean

• Geometric mean analyzes investment returns or growth rates over multiple periods, using compounding and reinvestment.
• Used to average rates of change over time or to compute a variable's growth rate.

The Weighted Mean

• Think of the weighted arithmetic mean as a way of finding an average (like you would with regular grades), but with a twist. In a regular average, every piece of information gets the same importance.
• With a weighted average, some pieces of information count more than others.

Harmonic Mean

• Appropriate when variabe is a rate or a ration, to find a fair average that will consider the comparisons in the proportion
• Calculated by summing reciprocating, averaging reciprocal and multiplying the number of observations

The Median

• Median, is the value of the middle item if it was set into ascending and descending order.
• Advantage, unlike the most that an extreme value will not affected it.

Mode

• Is the value the most frequesntly occuring value within a distribution.
• Distributions:
  • Unimodal, single value most frequently occuring
  • Bimodal, with two frequent values
  • Trimodal, with three occuring frequent values

Measure of Central Tendency

• When do you use each kind of mean?
  • consider if you want the outliers to be used, symmetry, compounding and extreme outliers.
• Other measures of location quantiles
  • quantile, a vaule below data lies, also known as a fractice.
  • quartiles, distributes into four equal parts
  • quintiles, distributes into even five parts
  • desciles, distributes evenly into ten quantiles
  • percentiles are quantiles that distribute 100 equal parts and equal the sum to 100.

Quantiles

• Are used for portfolio performance as well as stratgies for investment and research.

Measures of dispersion

• Discussing the variability around central tendency how spread out or variable those number around the avareged from that average

• We need to understand the returns dispersed around the mean.

• range, Mean absolute deviation, variance, and standard deviation,

• Why does it matter when investing? if consider an investment a measure an average for the central tendency is not enough if how much you are willing to invest. a high dispersion will indicated a larger risk since the reutn will vary by a wide range with the low reutrns more predicitable

Range

• The measure of dispersion is defined as the difference between the maximum and minimum values within the datase.
  • Range = Maximum - Minimum
• It should be noted here that "THE RANGE CANNOT TELL USE DATA HOW IT IS DISRIBUTED".

Mean Absolute Deviation

• the average distance between observations and their mean